Checkers is an old standby, with simple rules that a young child can grasp. It is also a favorite with some adults who enjoy the challenge of developing strategies for winning. Dominoes is another game that both children and adults can enjoy. There are many variations of the game, from simply matching numbers to earning points with a complicated scoring system. Dominoes also can be used to build structures or rows for toppling.
While not a strictly a game, jigsaw puzzles are a fun way for two people to enjoy time together. Other puzzle games require motor skills, such as Jenga® and pickup sticks.
Backgammon requires an understanding of not only the complicated rules, but also a grasp of successful strategy. One of the challenges of this game is doubling, which is a way of wagering on the outcome. Chess is another two-player game with complicated strategy. While many people believe it is a game for geniuses, anyone with an interest in strategy can enjoy the game. Other strategy games for two include Othello®, mankala and Blokus®.